Position Vector, Displacement, Velocity and Acceleration

A body is simultaneously given two velocities, one $10 \mathrm{m}{\mathrm{s}}^{-1}$ due east and other $20 \mathrm{m}{\mathrm{s}}^{-1}$due north-west. Calculate the resultant velocity.

One of the rectangular components of an acceleration of $8 \mathrm{m}{\mathrm{s}}^{-2}$ is $4 \mathrm{m}{\mathrm{s}}^{-2}$. Calculate the other component in ${\mathrm{ms}}^{-2}$.

A train is moving eastward at $10 \mathrm{m}/\sec$. A waiter is walking eastward at $1.2\mathrm{m}/\sec$ and a fly is charging towards the north across the waiter's tray at $2 \mathrm{m}/\mathrm{s}$. What is the velocity of the fly relative to Earth. 

For the given values of acceleration vector, what will be the resultant magnitude of the acceleration?

$a_x= 11 m/s^2, a_y= 13 m/s^2$.

Give the answer in terms of $\mathrm{m}/{\mathrm{s}}^2$.

The resultant of two vectors is perpendicular to first vector of magnitude $6 \mathrm{N}$. If the resultant has magnitude $6\sqrt{3}\text{ N}$, then magnitude of second vector is ( Give answer in $\mathrm{N}$)

The vector joining the points $A\left(1, 1,-1\right)$ and $B\left(2,-3, 4\right)$ and pointing from $A$ to $B$ is

At which point of a projectile motion, acceleration and velocity are perpendicular to each other?

A particle has an initial velocity of $3\hat{\mathrm{i}}+4\hat{\mathrm{j}}$ and an acceleration of $0.4\hat{\mathrm{i}}+0.3\hat{\mathrm{j}}$. Its speed after $10 \mathrm{s}$ is

 How can we get the instantaneous acceleration vector from the given velocity vectors of a body in circular motion? Will this acceleration change the magnitude of velocity vector?

How will you find the direction of average acceleration of a moving body in 2D if the final and initial velocity vectors are given? Explain with the help of a diagram.

For the given values of acceleration vector, what will be the resultant magnitude of the acceleration?

$a_x= 11 m/s^2, a_y= 13 m/s^2$.

Which of the formula is magnitude of the acceleration vector?

What will be resultant acceleration if $a_x = 4 m/s^2 , a_y= 3 m/s^2?$

Derive the expression for angle between acceleration vector and one of its component vectors when components are given.

For motion in two or three dimensions, velocity and acceleration vectors may have any angle between 0° and _____ between them.

Direction of average acceleration in vector in two dimensions is always in the direction of change in velocity vector.

A particle starts form the origin at $t=0$, with a velocity $5.0 \hat{i} {\mathrm{ms}}^{-1}$. When a certain force is applied on it, the position of the particle is $r\left(t\right)=\left(5.0t+1.5t^2\right) \hat{i}+1.0t^2 \hat{j}$. What is the velocity of the particle at $t=6 \mathrm{s}$?

The position of the particle is given by $r=3.0t \hat{i}+2.0t^2 \hat{j}+5.0 \hat{k}$ where $t$ is in seconds. Find the magnitude and direction of the $V\left(t\right)$ at $t=1.0 \mathrm{s}$.